Generic superconducting phase behavior in high-${\mathit{T}}_{\mathit{c}}$ cuprates: ${\mathit{T}}_{\mathit{c}}$ variation with hole concentration in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

A direct determination of the relationship between ${\mathit{T}}_{\mathit{c}}$ and hole concentration p for ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ca}}_{\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ is obtained by investigating the properties of the fully oxygen-deficient (δ≊1.0) compound for which p=x/2. Measurements of ${\mathit{T}}_{\mathit{c}}$, the thermoelectric power S, and bond-valence sums calculated from neutron-diffraction refinements for various values of x and δ allow the full determination of the relations p=p(δ), ${\mathit{T}}_{\mathit{c}}$=${\mathit{T}}_{\mathit{c}}$(p), and S=S(T,p) confirming that ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ satisfies the same universal relations in these quantities as the other high-${\mathit{T}}_{\mathit{c}}$ superconducting cuprates.